I have looked at the electoral politics of immigration for some time now. There is ambiguous evidence that opposing Amnesty is winning proposition for Republicans (at least in recent years). However, the reverse is decisive. Supporting Amnesty is a strong losing proposition for Republicans. It also appears that opposing Amnesty/supporting immigration control is a winning stand for Democrats.
In the 2006 elections, Republicans with F grades on immigration suffered far more severe losses (25% were defeated) than those with A grades (10% were defeated). Only 6.7% of the Immigration Reform Caucus was defeated. Notably, Lincoln Chafee was crushed even though he was liberal on everything including Amnesty. Dewine in Ohio suffered a similar fate for similar reasons.
Several immigration reformers including John Hostettler, Randy Graf, and J.D. Hayworth, were defeated. However, their Democratic opponents at least claimed to be tougher on immigration than they were (we will see). Indeed, many successful Democrats ran far to the right of their Republican opponents on immigration.
Two of the defeated Republicans (Graf, Hayworth) were in Arizona. Arizona had four immigration related initiatives on the ballot in 2006. All passed by huge margins. Clearly, immigration control was / is a very popular theme in Arizona . See here [PDF] and here for Democratic Underground discussion.
There overall model appears to be, that opposing Amnesty and supporting immigration enforcement is a big plus for Democrats. This position attracts blue collar workers, Republicans concerned about immigration, law and order types, etc. It probably alienates some ethnic activists. However, they aren't going to vote Republican anyway (Rove needs to consider rehab).
Conversely, supporting Amnesty/Open Borders is a strong loser for Republicans. Of course, Open Borders appeals to ethnic activists and corporate types. However, they are tied to the Democratic and Republican parties and won't switch over this issue. Conversely, Republican support for Open Borders is a strong "go to H...." message for blue collar workers, independents, middle-class voters concerned about schools, congestion, community values, etc.
This has been born out recently, by the dramatic falls in the popularity of McCain (falling from 59% to 48% approval), Bush (15% approval on immigration), and Mel Martinez (falling from 48% to 37% approval) as the Amnesty debate has proceeded. This is one issue that really "splits the blanket" for Republican voters.
As stated above, there are only limited recent examples of Republicans winning on an immigration control platform. Bilbray in California is a good example. Why? Of course, the Republican Party (starting with Bush) has sent a dubious message on the topic and Democrats have been able to easily outflank Republicans.
Back in 1994, this clearly wasn't the case. Pete Wilson scored a stunning come from (way) behind victory by attacking Open Borders. A key point is that immigration control was a "public" issue back then in California. It may be a "public" issue nationally now.